The first extra-solar planet around a main sequence star (i.e., not a neutron star or white dwarf) was found around the star 51 Pegasi in 1995. The large planet causes a measureable motion of the star around the center of mass of the system. Pegasi 51's orbital motion had a period of 4 days indicating a very large planet very close to the star. A large planet of mass M around a small star of mass 4M. The distance between planet and star is L. Both the planet and star will orbit around the center of mass of the system (marked by the red X).

Required:
Where is the center of mass of the star-planet system?

Answers

Answer 1

Answer:

   [tex]r_{cm}[/tex]= 1/5 L

Explanation:

To find the center of mass of the system let's use

        [tex]r_{cm} = \frac{1}{M}[/tex] ∑ r_i x_i

where m is the total mass of the system

let's apply this expression to our case

       

Let's set the reference frame on the star

         [tex]r_{cm} = \frac{1}{M +4M} ( 4M 0 + M L)[/tex]

         r_{cm} = [tex]\frac{1}{5}[/tex] L

         [tex]r_{cm}[/tex]= 1/5 L

Hey, the breast center is 1/5 of the distance between the star and the planet.


Related Questions

A ball is thrown straight up from ground level. It passes a 2-m-high window. The bottom of the window is 7.5 m off the ground. The time that elapses from when the ball passes the bottom of the window on the way up, to when it passes the top of the window on the way back down is 1.3 s.
What was the ball’s initial speed, in meters per second?

Answers

Answer:

[tex]u=14.48m/s[/tex]

Explanation:

From the question we are told that:

Height of window [tex]h=2m[/tex]

Height of window off the ground [tex]h_g=7.5m[/tex]

Time to fall and drop [tex]t=1.3s[/tex]

 

Generally the Newton's equation motion  is mathematically given by

 [tex]s=ut+\frac{1}{2}at^2[/tex]

Where

[tex]h=ut+\frac{1}{2}at^2[/tex]

[tex]2=u1.3-\frac{1}{2}*9.8*1.3^2[/tex]

[tex]2=u1.3-8.281[/tex]

[tex]u=7.91m/s^2[/tex]  

Generally the Newton's equation motion  is mathematically given by

[tex]2as=v^2-u^2[/tex]

Where

[tex]-2gh_g=v^2-u^2[/tex]

[tex]-2*9.8*7.5=(7.91)^2-u^2[/tex]

[tex]-147=62.5681-u^2[/tex]

[tex]u=\sqrt{209.5681}[/tex]

[tex]u=14.48m/s[/tex]

Therefore the  ball’s initial speed

[tex]u=14.48m/s[/tex]

What does the Curl-up test assess?
O A.
Body composition
ОВ.
Muscular strength and endurance
O C. Flexibility
D.
Cardiovascular fitness

HURRRY
(it’s pe not physics)

Answers

muscular strength and endurance!

Answer:

assesses C.) muscular endurance

Explanation:

1. Objects become electrically charged as a result of the transfer of

Answers

Answer:

Electron

Explanation:

An object can become electrically charged when it gains or loses an electron. Because an electron is negatively charged, when an object gains an electron it becomes negatively charged. Also, when it gives up an electron, it becomes positively charged. This positive charge is because the atom has one proton more than electron. In a neutral atom, the number of the proton is equal to the number of the electron. An electron is negatively charged, and a proton is positively charged.

A rock falls from a cliff and hits the ground at a velocity of 31m/s. How long did it take to fall?

Answers

Answer:

i dont know  man

Explanation:

i dont know man

Why are some tsunamis described as local?

Answers

Answer:

A local tsunami is one that originates from within about 100 km or less than 1 hour tsunami travel time from the impacted coastline. Local tsunamis can result in a significant number of casualties since authorities have little time to warn/evacuate the population.

Explanation:

Hope this helps

Urgent!!!!! A student heated 235 g of water in a beaker until the water reached 100°C. The student removed the beaker from the heat and placed the beaker on a counter in a 23°C room. The student recorded the temperature of the water every 4 minutes for 20 minutes. The data are shown in the table. Estimate the average temperature of the air in the room at 20 min. explain your answer.

Answers

It’s says that the temperature in the room is 23C so the air temperature in the air would be 23C

The average temperature of the air in the room at 20 min is 23°C.

What is temperature?

Temperature is the degree of hotness or coldness of the object.

A student heated 235 g of water in a beaker until the water reached 100°C. The student removed the beaker from the heat and placed the beaker on a counter in a 23°C room. The student recorded the temperature of the water every 4 minutes for 20 minutes.

The surrounding is vast, its temperature does not get affected by small amount of water. So, the temperature of air remains constant.

Thus, the average temperature of the air in the room at 20 min is 23°C.

Learn more about temperature.

https://brainly.com/question/11464844

#SPJ2

A skater spins with an angular speed of 5.9 rad/s with her arms outstretched. She lowers her arms, decreasing her moment of inertia by a factor of 1.7. Ignoring friction on the skates, determine the ratio of her final kinetic energy to her initial kinetic energy.

Answers

Answer:

the ratio of her final kinetic energy to her initial kinetic energy is 1.7.

Explanation:

Given;

initial angular speed, ω₁ = 5.9 rad/s

let her initial moment of inertia = I₁

her final moment of inertia [tex]I_2 = \frac{I_1}{1.7}[/tex]

Apply the principle of conservation of angular momentum to determine the final angular speed of the girl;

[tex]\omega_1I_1 = \omega_f I_2\\\\\omega_f = \frac{\omega _1 I_1}{I_2} \\\\\omega_f = \frac{5.9 \times I_1}{I_1/1.7} \\\\\omega = 5.9 \times 1.7 \\\\\omega_f = 10.03 \ rad/s[/tex]

The initial rotational kinetic energy is given as;

[tex]K.E_I = \frac{1}{2}I_1 \omega_I ^2[/tex]

The final rotational kinetic energy is given as;

[tex]K.E_f = \frac{1}{2}I_2 \omega_f ^2[/tex]

The ratio of her final kinetic energy to her initial kinetic energy is given as;

[tex]\frac{K.E_f}{K.E_I}= \frac{\frac{1}{2}I_2 \omega_f^2 }{\frac{1}{2} I_1\omega _1^2} \\\\\frac{K.E_f}{K.E_I}= \frac{I_2 \omega_f^2}{ I_1\omega _1^2} \\\\\frac{K.E_f}{K.E_I}= \frac{I_1/1.7 \times \omega_f^2}{ I_1 \times \omega _1^2} \\\\\frac{K.E_f}{K.E_I}= \frac{ \omega_f^2}{ 1.7 \omega _1^2} \\\\\frac{K.E_f}{K.E_I}= \frac{ (10.03)^2}{ 1.7(5.9)^2} = \frac{17}{10} = 1.7[/tex]

Therefore, the ratio of her final kinetic energy to her initial kinetic energy is 1.7.

A toy car rolls down a ramp. Which force causes the car to move

Answers

Answer:

Gravity

Explanation:

Gravity pulls things down to earth and it is a force

what is friction and the types withe examples.​

Answers

Explanation:

The answer is In the picture. Thanks.

10 POINTS!! SPACE QUESTION!!

Answers

The First one trust...

Answer: A (first option)

Explanation: In general, the surface temperatures decreases with increasing distance from the sun. Any warm object in space loses heat via infrared radiation; also visible radiation if it is hot enough. The hotter is the object, the faster it loses heat. Consequently any object warmed by the Sun stays at equilibrium temperature - it warms up until the radiative heat loss equals to the heat received, and cannot get any warmer beyond that.

What order shows increasing frequency for gamma rays, microwaves, visible light, and X-rays?

gamma rays, X-rays, visible light, microwaves
microwaves, visible light, X-rays, gamma rays
visible light, gamma rays, microwaves, X-rays
X-rays, microwaves, gamma rays, visible light

Answers

Answer:

B. microwaves, visible light, X-rays, gamma rays

The order that shows increasing frequency for gamma rays, microwaves, visible light, and X-rays is:

microwaves, visible light, X-rays, gamma rays

What are electromagnetic waves?

These are waves that can propagate (i.e travel) through space while transferring energy. They travel through space with the speed of light (i.e 3×10⁸ m/s)

Examples of electromagnetic waves includes

Gamma rayX-rayUltraviolet Light Infrared Radio wave Microwave

From the examples given above, it should be noted that gamma ray has the shortest wavelength and the longest frequency.

With the above information in mind, we can conclude that the order that shows increasing frequency for gamma rays, microwaves, visible light, and X-rays is:

microwaves, visible light, X-rays, gamma rays

Learn more about electromagnetic waves:

https://brainly.com/question/8553652

difference between concave and convex lens​

Answers

Answer:

convex lens:converging lens

focal length:positive

magnification; positive

concave lens:diverging lend

focal length:negative

magnification :negative

types:concavoconcave,planoconcave

A convex lens or converging lens focuses the light rays to a specific point whereas a concave lens or diverging lens diverges the light rays. A lens is a transparent material (either curved or flat surface) based on the principles of refraction. Concave lenses and convex lenses are often used together which is known as the Concave – Convex lens. When these lenses are combined, they produce sharper images. Most of the eyeglass lenses use combinations of convex and concave lenses. Cameras, telescopes and microscopes use different lens, helping us to see the world in a better

Read it and make it as table.

Which of the following is an example of kinetic energy being converted to potential energy?

Answers

Of the following...?? Is there more to this question? :)

Answer:

not completed questions

What is the magnitude and direction of the net force on a ball that has a force of 27N North and 18N North applied to it?

Answers

Answer:

Magnitude: =  32.45 Direction: =  33.69

Explanation:

The magnitude of the net force acting on an object is equal to the mass of the object multiplied by the acceleration of the object, as shown in this formula. We find its magnitude using the Pythagorean Theorem or the distance formula, and we find its direction using the inverse tangent function. Given a position vector →v=⟨a,b⟩, the magnitude is found by |v|=√a2+b2. The direction is equal to the angle formed with the x-axis, or with the y-axis, depending on the application.

what produces the distinctive flame color of different substances when they are ignited?

Answers

Answer:

Electrons in different metals

Explanation:

When you heat an atom, some of its electrons are "excited* to higher energy levels. When an electron drops from one level to a lower energy level, it emits a quantum of energy.  The different mix of energy differences for each atom produces different colours. Each metal gives a characteristic flame emission spectrum.

A 06-C charge and a .07-C charge are apart at 3 m apart. What force attracts them?

Answers

Answer:

F = 37.8 × 10^(6) N

Explanation:

The charges are 0.06 C and 0.07 C.

Thus;

Charge 1; q1 = 0.06 C

Charge 2; q2 = 0.07 C

Distance between them; r = 3 m

Formula for the force in between them is;

F = kq1•q2/r²

Where k is a constant = 9 × 10^(9) N.m²/C²

Thus;

F = (9 × 10^(9) × 0.06 × 0.07)/3²

F = 37.8 × 10^(6) N

why are the nuclei of the heavier elements radioactive and not the lighter elements of nuclei?

Answers

Answer:

becouse most of nuclear elements are heave

Explanation:

A sprinter accelerates at 8mps, he weights 850 grams. What
force is he exerting?

Answers

You do mass times weight, 8 times 850= 6,800. So the answer is 6,800.

Average running speed is 8km/h. Convert this to m/s :
a)8m/s
b)2.2m/s
c)28.8m/s
d)8km/h

Answers

Answer:

Im not sure if you mean miles per hour or meters per hour but if it is miles it is 4.97 miles per hour and if it is meters then it is 8000 meters per hour

Explanation:

Sorry if I'm wrong

A 20-kg child is on top of a slide was pushed down by his brother giving him an initial speed of 2 m/s down the slide. what is the child's speed at the bottom of the slide if the slide is 5 m high and 10m long and the force of friction between the child and slide is negligible?​

Answers

Answer:

please find your answer in the attached picture, along with explanation.

ILL GIVE BRAINLIST PLS In which circuit does charge reverse direction many times per second?
A. A DC circuit
B. A combined circuit
C. A parallel circuit D. An AC circuit

Answers

Answer: D. An AC circuit

Explanation:

I took it on a test and it was correct ; )

A rabbit dashes across a field in a zig-zag pattern trying to outrun a fox. If the rabbit’s average is speed is 9.8 m/s it reaches the hole in 8.5 s what is the total distance it ran?

Answers

Answer:

83.3 m

Explanation:

From the question,

Applying on of the formula of velocity

V = d/t.................. Equation 1

Where V = average velocity, d = distance, t = time.

make d the subject of the equation

d = V×t................. Equation 2

Given: V = 9.8 m/s, t = 8.5 s

Substitute these values into equation 2

d = 9.8×8.5

d = 83.3 m

Hence the total distance covered by the rabbit is 83.3 m

Consider a wheel (solid disk) of radius 1.12 m, mass 10 kg and moment of inertia 1 2 M R2 . The wheel rolls without slipping in a straight line in an uphill direction 37◦ above the horizontal. The wheel starts at angular speed 12.0536 rad/s but the rotation slows down as the wheel rolls uphill, and eventually the wheel comes to a stop and rolls back downhill. How far does the wheel roll in the uphill direction before it stops?

Answers

Answer:

d= 23.25 m

Explanation:

Assuming no other external forces acting on the disk, total mechanical energy must be conserved.Taking the initial height of the disk as the zero reference for the gravitational potential energy, initially. all the energy is kinetic.This kinetic energy is part translational kinetic energy, and part rotational kinetic energy, as follows:

       [tex]E_{o} = K_{transo} + K_{roto} (1)[/tex]

When the disk rolling uphill finally comes to an stop, its energy is completely gravitational potential energy, as follows:

       [tex]E_{f} = m*g*h (2)[/tex]

Since the angle with the horizontal of the track on which the disk is rolling, is 37º, we can express the height h in terms of the distance traveled d and the angle of 37º, as follows:

       [tex]h = d* sin 37 (3)[/tex]

Replacing (3) in (2):

       [tex]E_{f} = m*g* d * sin 37 (4)[/tex]

Since the wheel rolls without sleeping, this means that at any time there is a fixed relationship in the translational speed and the angular speed, as follows:

       [tex]v = \omega * R (5)[/tex]

For a solid disk, as mentioned in the question, the moment of inertia is just 1/2*M*R².The rotational kinetic energy of a rotating rigid body can be written as follows:

       [tex]K_{rot} = \frac{1}{2}* I * \omega^{2} (6)[/tex]

Replacing I from (6) and ω from (5), and remembering the definition of the translational kinetic energy, we can solve (1) in terms of v, m and r as follows:

       [tex]E_{o} = K_{transo} + K_{roto} = \frac{1}{2}* m* v^{2} +(\frac{1}{2}* \frac{1}{2}) *m*r^{2}*(\frac{v}{r}) ^{2} = \\ \frac{3}{4} * m * v^{2} (7)[/tex]

Since (4) and (7) must be equal each other, we can solve for d as follows:

       [tex]d =\frac{3}{4} * \frac{v^{2}}{g*sin37} = \frac{3}{4}*\frac{(\omega*r)^{2}}{g*sin 37} (8)[/tex]

Replacing by the values, we finally get:

       [tex]d =\frac{3}{4}*\frac{(\omega*r)^{2}}{g*sin 37} = \frac{3}{4} *\frac{(12.0536rad/sec*1.12m)^{2}}{9.8 m/s2*0.601} = 23. 25 m.[/tex]

If the girl skater has a mass of 30 kg and moves backward at 5 m/s, what is the velocity or the boy skater
his mass is 50 kg?

Answers

Question: Two people stand facing each other at a roller-skating rink then push off each other. If the girl skater has a mass of 30 kg and moves backward at 5 m/s, what is the velocity of the boy skater if his mass is 50 kg?

Answer:

3 m/s

Explanation:

Applying,

The Law of conservation of momentum

Momentum of the girl skater = momentum of the boy skater

MV = mv...................... Equation 1

Where M = mass of the girl skater, V = velocity of the girl skater, m = mass of the boy skater, v = velocity of the boy skater

From the question, we were asked to calculate v

v = MV/m.................. Equation 1

Given: M = 30 kg, V = 5 m/s, m = 50 kg

Substitute these values into equation 1

v = (30×5)/50

v = 3 m/s

Hence the velocity of the the boy skater is 3m/s

the minimum speed on the interstate highway is
1. 40 mph
2. 60 mph
3. 55 mph
4. 50 mph
I'm in Nebraska btw​

Answers

It’s 1 I’m not from Nebraska but I looked it up lol.

Light with a wavelength of 700 nm (7×〖10〗^(-7) m) is incident upon a double slit with a separation of 0.30 mm (3 x 10-4 m). A screen is located 1.5 m from the double slit. At what distance from the screen will the first bright fringe beyond the center fringe appear?

Answers

Answer:

[tex]0.0035\ \text{m}[/tex]

Explanation:

y = Distance from the center point

d = Separation between slits = 0.3 mm

D = Distance between slit and screen = 1.5 m

[tex]\lambda[/tex] = Wavelength = 700 nm

m = Order = 1

We have the relation

[tex]d\dfrac{y}{D}=m\lambda\\\Rightarrow y=\dfrac{Dm\lambda}{d}\\\Rightarrow y=\dfrac{1.5\times 1\times 700\times 10^{-9}}{0.3\times 10^{-3}}\\\Rightarrow y=0.0035\ \text{m}[/tex]

The distance from the screen at which the first bright fringe beyond the center fringe appear is [tex]0.0035\ \text{m}[/tex].

1. A group of students were trying to find the greatest
rebounded height of a rubber ball dropped on a basketball
court. They dropped from 3 different heights. The chart
below has their data.
26 cm
Drop Height Chart
Trials Drop height Rebound height
Trial 12 meters 103 cm
Trial 2% meter
Trial 31 meter 58 cm
Which explanation is the best reason for why trial 1 has the
greatest rebound height?
A. The speed of the ball is determined by the distance it
travels.
B. The force applied to the ball is a balanced force.
C) The greater the force applied to the ball the greater the
change in motion.
D. The closer the ball is to the ground the more gravity it
has.

Answers

Answer:

D th

Explanation:

D B. The force applied to the ball is a balanced force.

A 35.0 g bullet strikes a 50 kg stationary piece of lumber and embeds itself in the wood. The piece of lumber and the bullet fly off together at 8.6 m/s. What was the speed of the ballot before it struck the lumbar? Define the bullet and the wood as a system

Answers

Answer:

12294.31 m/s

Explanation:

Momentum = (mass)(velocity)

Momentum before = Momentum after

(momentum of bullet)+(momentum of block)=(momentum of bullet and block)

0.035v+50(0)=(0.035+50)(8.6)

0.035v=430.301

v=12294.3142857m/s

1. If a system is isolated, the total energy within that system is constant. Consider the case of a hot cup of coffee: when it cools down, the energy goes into the surrounding air, causing the air to warm. If the coffee and the air are placed in an isolated chamber, the total energy of the system (coffee + air) is constant because the energy lost by the coffee is exactly equal to the energy gained by the air.
The only way for the total energy of a system to change is when it is not isolated, meaning that external forces or sources of energy interact with the system. If we want to define a system where the total energy is conserved, which one of the choices below would be the best system to consider?
A. The person
B. The person and the Earth
C. The Earth
2. Based on your answer to Question 1, why doesn’t the total energy of the Earth-person system change when the person goes up to a new height, gaining potential energy?

Answers

Answer:

1. B. The person and the Earth

2. This is because the energy gained by the person equals the energy lost by the earth,

Explanation:

1.

B. The person and the Earth

This is because the person and the earth both represent a system. A system consists of more than one item. A system consists of two or more items interacting with each other.

2. This is because, the energy of an isolated system is conserved according to the second law of thermodynamics which states that in an isolated system, energy can neither be created nor destroyed. So, there is an exchange of energy between the person and the Earth. So, the energy gained by the person at the new height equals the energy lost by the earth. And thus, the total energy of the system remains constant.

an object is moving at 60m/s and has a mass of 5 kg what is its momentum​

Answers

Answer:

300

Explanation:

the momentum is 300

p=mv

p=5×60

5×60 =300

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Hey can you help me fast!! One fourth of the 120 students took wood shop. How many students did not take wood shop? 2. When two species compete for the sameresource, they sometimes divide thisresource. This is an example ofa. niche partitioningb. niche equivalencyc. evolutionary response.d. ecological equivalence (6 or 7 points***) Please help!!!! really important to get done Look at the following Drawing and answer the questions using direct object pronouns. 9) Ves los pupitres?10) Me ves? How do scientists use GPS? Using Angle Relationships to Solve Equations The FM station broadcasts traditional music at 102 MHz on your radio units for FM frequencies are given in MHz. Find the wave length of radio station in metres (m), nanometre(nm) and angstrom(). solve y=f(x) for x then find the input when the output is 6 f(x)= 6x^2 find the 12th term of the geometric sequence show below x^2, -2x^6, 4x^10 Dr. Victory is a psychologist studying the effects of high-level classes, bullying, and music classes on the anxiety levels of middle school students. He has previously determined that the effects from class levels, bullying experiences, and music classes are independent. It has been determined that the probability that a student is taking a high-level English class is 0.23, the probability that a student has been bullied is 0.36, and 1/3 of students are in music classes.(a) What is the probability that a randomly selected student is in a high-level English class and has been bullied? (b) What is the probability that a randomly selected student is in a music class and has been bullied? (c) What is the probability that a randomly selected student is in a music class, has been bullied, and is in a high-level English class? The ratio of boys to girls in the 10th grade is 8 to 13. If there are 91 girls in 10th grade, then how many boys are there? GIVING BRAINILEST DONT BE ALL CRAZY FOR ME PLEASE. In one sentence, describe one reason for the decline of the Roman Empire. In a second sentence, describe whether or not this problem also occurred during the decline of the Roman Republic. 7. Find the length of HP.12P9H Napoleon was what type of military officer? A. ordinance OfficerB. Naval officerC. Cavalry officerD. Artillery office Generate a random protein sequence that is 5 amino acids long. Why did it require tremendous courage for Dr. King to speak in Montgomery, when the march was completed? Identify three ways that you are impacted by your state or local government. What are some services provided by these levels of government? Why doesn't the federal government take on more of this role? Your essay should mention the principles of federalism and limited government and explain how they apply to this question. plz help A, B, C, D ??? Please help ......help due in a minute You have $12,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 14 percent and Stock Y with an expected return of 10 percent. Assume your goal is to create a portfolio with an expected return of 12.30 percent. How much money will you invest in Stock X and Stock Y? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)You have $12,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 14 percent and Stock Y with an expected return of 10 percent. Assume your goal is to create a portfolio with an expected return of 12.30 percent. How much money will you invest in Stock X and Stock Y? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)